CERN-TH/2001-330 BOUND STATES IN n DIMENSIONS (Especially n = 1 and n = 2)
نویسندگان
چکیده
We stress that in contradiction with what happens in space dimensions n ≥ 3, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two dimensions, examples of weak potentials with one or infinitely many bound states. We derive bounds for one and two dimensions which have the “right” coupling constant behaviour for large coupling. CERN-TH/2001-330 November 2001
منابع مشابه
CERN-TH/98-330 NYU-TH/98/10/02 hep-th/9810063 N=6 Supergravity on AdS5 and the SU(2, 2/3) Superconformal Correspondence
It is argued that N=6 supergravity on AdS5, with gauge group SU(3) × U(1) corresponds, at the classical level, to a subsector of the “chiral” primary operators of N=4 Yang-Mills theories. This projection involves a “duality transformation” of N=4 Yang-Mills theory and therefore can be valid if the coupling is at a self-dual point, or for those amplitudes that do not depend on the coupling const...
متن کاملCern-th/2003-235 Bound States in Two Spatial Dimensions in the Non-central Case
We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the BirmanSchwinger bound in three dimensions. Specifically, counting the number of bound states in a potential gV for g = 1 is replaced by counting the number of gi’s for which zero energy bound states exist, and then the kernel...
متن کاملar X iv : m at h - ph / 0 20 80 11 v 1 6 A ug 2 00 2 CERN - TH / 2002 - 128 BOUND STATES IN ONE AND TWO SPATIAL DIMENSIONS
In this paper we study the number of bound states for potentials in one and two spatial dimensions. We first show that in addition to the well-known fact that an arbitrarily weak attractive potential has a bound state, it is easy to construct examples where weak potentials have an infinite number of bound states. These examples have potentials which decrease at infinity faster than expected. Us...
متن کامل2 00 1 Eth - Th / 01 - 11 Cern - Th / 2001 - 204 Limits on the Size of Extra Dimensions and the String Scale
We give a brief summary of present bounds on the size of possible extra-dimensions as well as the string scale from collider experiments.
متن کاملCERN-TH/2001-215 hep-ph/0108069
We study in this paper the production, in hadronic collisions, of final states with W gauge bosons, heavy quark pairs and n extra jets (with n up to 4). The complete partonic tree-level QCD matrix elements are evaluated using the ALPHA algorithm, and the events generated at the parton level are then evolved through the QCD shower and eventually hadronised using the coherent shower evolution pro...
متن کامل